What does Hedley Bull argue in his essay "Does Order Exist in World Politics?"

As your tag implies, Hedley Bull was a member of the
English School of international relations.  This school of thought is a constructivist
school of thought that does not completely reject realism but which criticizes that
school of thought.  This is what Bull is trying to say in this chapter -- he is trying
to say that there is such a thing as an international society and that states do not
exist merely in a Hobbesian state of anarchy.

Bull points
out that there has long been some degree of cooperation between states.  The actions of
states have also long been regulated by a set of standards that all states have been
expected to abide by.  This is not to say that states
always play by the rules or that they always cooperate. 
However, Bull is arguing that the realists are missing something when they argue that
the international system is characterized only by
anarchy.

So the major point of this chapter is that anarchy
is not the only characteristic of the international system.  Instead, states show a
strong tendency to cooperate with one another and to abide by unwritten "laws" that help
to constrain their actions.  Both of these ideas are contrary to what realists believe
should be the case.